Young Jun Lee

Young Jun Lee

Young Jun Lee - Website

Research interests

Primary: Econometric theory, nonparametric econometrics
Secondary: Time series, financial econometrics, applied microeconomics

Paper title - 'Sieve estimation of optimal transport with applications to multivariate quantiles and matching'

Abstract - This paper proposes a nonparametric estimator of the unique solution for the optimal transport problem. The optimal transport problem is basically to find a joint distribution or a deterministic function assigning one distribution to the other one with an optimality condition. Many problems in economics, including matching models and quantile methods, have the structure of an optimal transport problem. Under the existing conditions for uniqueness and regularity of the optimal transport, we propose sieve M-estimator solving the dual Kantorovich problem. We derive convergence rates for the estimator and its derivative. We can weaken conditions found in the existing literature substantially, and the derived convergence rates are the same as the optimal rate in the context of regression and density estimations. Our results can be extended to the conditional optimal transport problem and semiparametric two-step estimation involving sieve estimation of optimal transport in the first step. We apply these extensions to the conditional vector quantiles and multidimensional matching models, respectively. Our application with real data in Carlier et al. (2016) and Lindenlaub (2017) reveals interesting patterns.

References

• Dennis Kristensen (UCL)
• Daniel Wilhelm (UCL)
• Martin Weidner (UCL)